We study collective phenomena in highly heterogeneous cardiac cell culture and its models. A cardiac culture is a mixture of passive (fibroblasts), oscillatory (pacemakers), and excitable (myocytes) cells. There is also heterogeneity within each type of cell as well. Results of in vitro experiments are modelled by Luo-Rudy and FitzHugh-Nagumo systems. For oscillatory and excitable media, we focus on the transitions from fully incoherent behavior to partially coherent behavior and then to global synchronization as the coupling strength is increased. These regimes are characterized qualitatively by spatiotemporal diagrams and quantitatively by profiles of dependence of individual frequencies on coupling. We find that synchronization clusters are determined by concentric and spiral waves. These waves arising due to the heterogeneity of medium push covered cells to oscillate in synchrony. We are also interested in the influence of passive and excitable elements on the oscillatory characteristics of low- and high-dimensional ensembles of cardiac cells. The mixture of initially silent excitable and passive cells shows the transitions to oscillatory behavior. In the media of oscillatory and passive or excitable cells, the effect of oscillation death is observed.

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We study collective dynamics in rotator ensembles and focus on the multistability of synchronous regimes in a chain of coupled rotators. We provide a detailed analysis of the number of coexisting regimes and estimate in particular, the synchronization boundary for different types of individual frequency distribution. The number of wave-based regimes coexisting for the same parameters and its dependence on the chain length are estimated. We give an analytical estimation for the synchronization frequency of the in-phase regime for a uniform individual frequency distribution.

We study dynamical regimes in a two dimensional excitable medium driven by a cluster of nonidentical oscillatory elements inside of it. In general, similar topologies take place e.g. in heart, where Sino-Atrial Node (SAN) is surrounded by excitable cells of atrial tissue. Moreover, the topology of SAN of rabbit is effectively two dimensional due to very small thickness of tissue in that region. That makes this study even more plausible. Our numerical experiments with FitzHugh-Nagumo and Luo-Rudy I models show that instant pathological change in oscillatory cells can trigger drastical changes to the dynamical regimes of the whole lattice. Several mechanisms of that kind are presented and discussed in this paper. For instance, we show that increasing oscillatory elements' nonidentity can cause wave propagation defects resulting in the onset of the spiral waves in the excitable media.